[{"data":1,"prerenderedAt":12499},["ShallowReactive",2],{"indicators:functions/moving-averages":3},{"slug":4,"filePath":5,"frontmatter":6,"rawMarkdown":11,"tree":12},"functions/moving-averages","functions/moving-averages.md",{"title":7,"description":8,"order":9,"section":10},"Moving averages","These classes smooth price into a trend line or wrap it in a band. Every one of them ships in every workspace as part of src/sdk/ta.ts: the whole kScript…",32,"functions","---\ntitle: \"Moving averages\"\ndescription: \"These classes smooth price into a trend line or wrap it in a band. Every one of them ships in every workspace as part of src/sdk/ta.ts: the whole kScript…\"\norder: 32\nsection: \"functions\"\n---\n\n\u003C!-- source: docs/indicators/functions/moving-averages.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit -->\n\n# Moving averages\n\nThese classes smooth price into a trend line or wrap it in a band. Every\none of them ships in every workspace as part of `src/sdk/ta.ts`: the whole\nkScript (legacy) roster (`sma`, `ema`, `wma`, `hma`, `alma`, `swma`,\n`vwma`, `rma`, `linreg`, `bb`, `keltner`, `donchian`) is a class with the\nsame name in title case, each one built the same way: allocate in the\nconstructor, fold one bar per `update()`, return `NaN` until the window is\nfull, restore with `reset()`. Import the class you need from `./sdk/ta`,\nconstruct it in `init()`, and call `update()` once per bar in `state()`.\nEvery class mirrors the kScript engine's arithmetic and its edge rules, so\na port draws the same line bar for bar ([TA library](ta-library.md) lists\nthe full catalog and the proof).\n\nEvery windowed average is `NaN` until its window fills. An `Sma(20)` draws\nnothing for its first 19 bars, then begins once the 20th has loaded; the\nHull average warms up a little longer because of its internal weighted\nsub-windows. Donchian is the exception: it reads the rolling extreme of\nwhatever has loaded from the very first bar. `NaN` is the warm-up signal\non every host, so an abstaining `state()` (`return 0`) and a `NaN` written\nto one output are the two honest ways to say \"not yet\"\n([Execution model](../core-concepts/execution-model.md)).\n\nThe shape every class shares:\n\n| Member | Meaning |\n| --- | --- |\n| `new X(period)` | allocates the window once; a `period` below 1 is clamped to 1 |\n| `.update(x): f64` | folds one bar, returns the current value, `NaN` until warm |\n| `.reset(): void` | back to the freshly constructed state; call it from your `reset()` |\n\nA non-finite input (a `NaN` or an infinity) inside a window makes the\nwindowed averages return `NaN` for as long as that bar sits in the window;\nthe two running averages (`Ema`, `Rma`) never recover from one, which is\nthe engine's rule too.\n\n## Single-line averages\n\n### Sma\n\n`new Sma(period)`, `.update(x)`: the unweighted mean of the last `period`\nvalues, summed oldest to newest and divided by the period. Warm-up is\n`period` bars (first value at bar `period - 1`).\n\n```typescript\nimport { Sma } from \"./sdk/ta\";\n\nlet sma = new Sma(20);\nexport function init(): void { sma = new Sma(i32(p_period())); }\n```\n\nRead the period through its accessor and cast it: params are `f64`, class\nperiods are `i32`, and AssemblyScript refuses the implicit conversion.\n\n### Ema\n\n`new Ema(period)`, `.update(x)`: the exponential average. Weights recent\nbars more heavily, so it turns faster than `Sma`. The first `period`\nfinite values seed it with their simple mean, then `x * alpha + prev * (1\n- alpha)` with `alpha = 2 / (period + 1)` takes over, so it is `NaN` for\n`period - 1` bars. A non-finite input before the seed completes restarts\nthe seed count; one after the seed sets the value to `NaN` for good (the\nengine never reseeds).\n\n```typescript\nimport { Ema } from \"./sdk/ta\";\n\nlet ema = new Ema(20);\n```\n\n### Wma\n\n`new Wma(period)`, `.update(x)`: the linearly weighted average. The newest\nbar carries weight `period`, the oldest weight `1`, so it sits between\n`Sma` and `Ema` in responsiveness. The weighted sum walks oldest to newest\nand is divided by `period * (period + 1) / 2`; `NaN` until `period` bars\nhave been seen and whenever any value in the window is not finite.\n\n```typescript\nimport { Wma } from \"./sdk/ta\";\n\nlet wma = new Wma(20);\nexport function init(): void { wma = new Wma(i32(p_period())); }\n```\n\n### Hma\n\n`new Hma(period)`, `.update(x)`: the Hull average, three `Wma` windows\ncomposed as `WMA(2 * WMA(round(n / 2)) - WMA(n), round(sqrt(n)))`. Very\nlow lag and smooth. The half and square-root lengths are rounded (never\nbelow 1), the inner difference is `NaN` until both inner windows are warm,\nand the outer window then needs `round(sqrt(n))` finite values, so the\nfirst value lands at bar `n - 1 + round(sqrt(n)) - 1`.\n\n```typescript\nimport { Hma } from \"./sdk/ta\";\n\nlet hma = new Hma(21);\nexport function init(): void { hma = new Hma(i32(p_hull_period())); }\n```\n\n### Alma\n\n`new Alma(length, offset = 0.85, sigma = 6)`, `.update(x)`: the Arnaud\nLegoux average, a Gaussian-weighted window. `offset` places the peak of\nthe bell at `offset * (length - 1)` from the oldest bar (near the newest\nbar by default), `sigma` sets its width as `length / sigma`. The weights\nare computed once in the constructor with the engine's arithmetic, so\n`update()` is a single weighted pass, walked oldest to newest. `NaN` until\n`length` bars have been seen and whenever any value in the window is not\nfinite.\n\n```typescript\nimport { Alma } from \"./sdk/ta\";\n\nlet alma = new Alma(20);              // offset 0.85, sigma 6\nlet sharp = new Alma(20, 0.9, 4.0);   // peak closer to the newest bar, narrower bell\n```\n\nOmitting `offset` and `sigma` is the same as passing `0.85` and `6`; the\nconstructor defaults are the kScript defaults.\n\n### Swma\n\n`new Swma()`, `.update(x)`: the symmetrically weighted average, the fixed\nfour-tap smoother `(x[3] + 2 * x[2] + 2 * x[1] + x[0]) / 6` with `x[0]`\nthe newest bar. `NaN` on the first three bars (first value at bar 3) and\nwhenever any of the four values is not finite; no period to choose.\n\n```typescript\nimport { Swma } from \"./sdk/ta\";\n\nlet swma = new Swma();\n```\n\n### Vwma\n\n`new Vwma(period)`, `.update(price, volume)`: the volume-weighted average\ntakes two values per bar, `sum(price * volume) / sum(volume)` over the\nwindow. Bars with more volume pull the average harder, so it tracks where\ntrading actually happened. It needs a volume input beside the price input\n(`input(\"volume\", ohlcv.volume)`). `NaN` until `period` bars have been\nseen, whenever any price or volume in the window is not finite, and when\nthe volume sum is exactly `0`.\n\n```typescript\nimport { Vwma } from \"./sdk/ta\";\n\nlet vwma = new Vwma(20);\nexport function state(): i32 {\n  const value = vwma.update(in_close(), in_volume());\n  return isNaN(value) ? 0 : 1;\n}\n```\n\n### Rma\n\n`new Rma(period)`, `.update(x)`: the running (Wilder) average, the\nsmoothing inside RSI and ATR. The first `period` finite values seed it\nwith their simple mean, then `rma = (rma * (period - 1) + x) / period`.\nSmoother and slower than `Ema` for the same period. This is the same\nWilder accumulator the kScript engine runs and the one `Rsi` and `Atr`\nuse internally, so an RSI built by hand over `Rma` and the shipped `Rsi`\nagree. A non-finite input before the seed completes restarts the seed\ncount; one after the seed sets the value to `NaN` for good.\n\n```typescript\nimport { Rma } from \"./sdk/ta\";\n\nlet rma = new Rma(14);\n```\n\n### Linreg\n\n`new Linreg(period, offset = 0)`, `.update(x)`: linear regression fits a\nleast-squares line over the last `period` bars (x positions `0` oldest to\n`period - 1` newest) and returns its value at the newest bar (`offset`\n`0`) or `offset` bars back along the fitted line: the trend's fitted price\nrather than an average. `offset` is an `f64` truncated to an integer. `NaN`\nuntil `period` bars have been seen and whenever any value in the window\nis not finite; a period of `1` returns the value itself.\n\n```typescript\nimport { Linreg } from \"./sdk/ta\";\n\nlet linreg = new Linreg(20);        // value at the newest bar\nlet lagged = new Linreg(20, 2.0);   // the fitted line two bars back\n```\n\n## Band helpers\n\nA kScript band helper returned three named streams. An Indicator has no\ntuple outputs: the class exposes `upper`, `basis`, and `lower` as fields\nafter each `update()`, and you write each one to its own output\n([Named streams](../core-concepts/named-streams.md)). Shading between the\nedges is a `box` on every bar ([Drawing primitives](drawing-primitives.md)).\n\n### Bb\n\n`new Bb(period, mult)`, `.update(x)`: Bollinger bands. `basis` is the\nwindow mean (the same arithmetic as `Sma`), `upper` and `lower` sit `mult`\npopulation standard deviations away (the same arithmetic as `Stdev`, the\ntextbook Bollinger form). `update()` returns the basis and fills the three\nfields. All three are `NaN` until `period` bars exist and whenever any bar\nof the window is not finite; the window heals as soon as the bad bar\nleaves it. Both arguments are required; kScript's usual call is\n`new Bb(20, 2.0)`.\n\n```typescript\nimport { Bb } from \"./sdk/ta\";\n\nlet bb = new Bb(20, 2.0);\nexport function finalize(): void {\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n  emitRow();\n}\n```\n\n### Keltner\n\n`new Keltner(period, mult, atrPeriod)`, `.update(x, high, low, close)`:\nlike Bollinger, but the width comes from the average true range instead\nof the standard deviation, so it reacts to range rather than dispersion.\n`basis` is an `Ema(period)` over `x` (usually the close), the width is an\n`Atr(atrPeriod)` over the three prices (the Wilder-smoothed true range;\nits class is on the [Trend indicators](trend-indicators.md) page)\nmultiplied by `mult`. `update()` returns the basis and fills the three\nfields. The basis is reported as soon as the `Ema` is seeded, even while\nthe ATR is still warming up; `upper` and `lower` are `NaN` unless both the\nbasis and the ATR are finite.\n\n```typescript\nimport { Keltner } from \"./sdk/ta\";\n\nlet kc = new Keltner(20, 1.5, 10);\nexport function state(): i32 {\n  const close = in_close();\n  kc.update(close, in_high(), in_low(), close);\n  return 1;\n}\n```\n\n### Donchian\n\n`new Donchian(period = 12)`, `.update(high, low)`: the highest high and\nlowest low over `period` bars as `upper` and `lower`, with their midpoint\nas `basis` (the value `update()` returns; the kScript builtin returns only\nthe midline). Because it reads the rolling extreme rather than averaging,\nit is finite from the first loaded bar: the window is partial at the\nstart, and bar 0 returns `(high + low) / 2` of that bar alone. The current\nbar's high and low always take part, even when `NaN` (so a `NaN` bar\npropagates), while non-finite highs or lows of older bars are skipped.\n\n```typescript\nimport { Donchian } from \"./sdk/ta\";\n\nlet dc = new Donchian(20);\nexport function state(): i32 {\n  dc.update(in_high(), in_low());\n  return 1;\n}\n```\n\n## Putting them together\n\nEvery average and band on one chart: the nine single-line averages on the\nprice pane, the three band helpers as nine more outputs. Every class comes\nfrom `./sdk/ta` in one import line. Each class is constructed in `init()`\nfrom a param, updated once in `state()`, and its value written in\n`finalize()`.\n\n```typescript\nimport { input, line, ohlcv, output, overlay, param } from \"./sdk/declare\";\nimport { in_close, in_high, in_low, in_volume } from \"./gen/inputs\";\nimport {\n  emitRow,\n  out_alma,\n  out_bb_basis,\n  out_bb_lower,\n  out_bb_upper,\n  out_dc_basis,\n  out_dc_lower,\n  out_dc_upper,\n  out_ema,\n  out_hma,\n  out_kc_basis,\n  out_kc_lower,\n  out_kc_upper,\n  out_linreg,\n  out_rma,\n  out_sma,\n  out_swma,\n  out_vwma,\n  out_wma,\n} from \"./gen/outputs\";\nimport { p_atr_period, p_hull_period, p_kc_mult, p_mult, p_period } from \"./gen/params\";\nimport { Alma, Bb, Donchian, Ema, Hma, Keltner, Linreg, Rma, Sma, Swma, Vwma, Wma } from \"./sdk/ta\";\n\nparam(\"period\", 20, { min: 2, max: 400, description: \"Window for every average and band\" });\nparam(\"hull_period\", 21, { min: 4, max: 400, description: \"Hull average window\" });\nparam(\"mult\", 2, { min: 0.5, max: 5, description: \"Bollinger standard-deviation multiplier\" });\nparam(\"kc_mult\", 1.5, { min: 0.5, max: 5, description: \"Keltner ATR multiplier\" });\nparam(\"atr_period\", 10, { min: 1, max: 200, description: \"Keltner ATR window\" });\ninput(\"close\", ohlcv.close);\ninput(\"high\", ohlcv.high);\ninput(\"low\", ohlcv.low);\ninput(\"volume\", ohlcv.volume);\noutput(\"sma\", line, overlay, { color: \"#2563eb\", width: 2, description: \"Simple moving average\" });\noutput(\"ema\", line, overlay, { color: \"#dc2626\", width: 2, description: \"Exponential moving average\" });\noutput(\"hma\", line, overlay, { color: \"#7c3aed\", width: 2, description: \"Hull moving average\" });\noutput(\"wma\", line, overlay, { color: \"#ea580c\", width: 2, description: \"Weighted moving average\" });\noutput(\"alma\", line, overlay, { color: \"#0891b2\", width: 2, description: \"Arnaud Legoux moving average\" });\noutput(\"swma\", line, overlay, { color: \"#0f766e\", width: 1, description: \"Symmetrically weighted moving average\" });\noutput(\"vwma\", line, overlay, { color: \"#b45309\", width: 2, description: \"Volume-weighted moving average\" });\noutput(\"rma\", line, overlay, { color: \"#059669\", width: 2, description: \"Wilder running moving average\" });\noutput(\"linreg\", line, overlay, { color: \"#4b5563\", width: 2, description: \"Least-squares regression value\" });\noutput(\"bb_upper\", line, overlay, { color: \"#0f766e\", width: 1, description: \"Bollinger upper band\" });\noutput(\"bb_basis\", line, overlay, { color: \"#64748b\", width: 1, description: \"Bollinger basis\" });\noutput(\"bb_lower\", line, overlay, { color: \"#be123c\", width: 1, description: \"Bollinger lower band\" });\noutput(\"kc_upper\", line, overlay, { color: \"#16a34a\", width: 1, description: \"Keltner upper channel\" });\noutput(\"kc_basis\", line, overlay, { color: \"#94a3b8\", width: 1, description: \"Keltner basis\" });\noutput(\"kc_lower\", line, overlay, { color: \"#dc2626\", width: 1, description: \"Keltner lower channel\" });\noutput(\"dc_upper\", line, overlay, { color: \"#0ea5e9\", width: 1, description: \"Donchian upper band\" });\noutput(\"dc_basis\", line, overlay, { color: \"#94a3b8\", width: 1, description: \"Donchian midpoint\" });\noutput(\"dc_lower\", line, overlay, { color: \"#f97316\", width: 1, description: \"Donchian lower band\" });\n\nlet sma = new Sma(20);\nlet ema = new Ema(20);\nlet hma = new Hma(21);\nlet wma = new Wma(20);\nlet alma = new Alma(20);\nlet swma = new Swma();\nlet vwma = new Vwma(20);\nlet rma = new Rma(20);\nlet linreg = new Linreg(20);\nlet bb = new Bb(20, 2.0);\nlet kc = new Keltner(20, 1.5, 10);\nlet dc = new Donchian(20);\nlet smaValue: f64 = NaN;\nlet emaValue: f64 = NaN;\nlet hmaValue: f64 = NaN;\nlet wmaValue: f64 = NaN;\nlet almaValue: f64 = NaN;\nlet swmaValue: f64 = NaN;\nlet vwmaValue: f64 = NaN;\nlet rmaValue: f64 = NaN;\nlet linregValue: f64 = NaN;\n\nexport function init(): void {\n  const period = i32(p_period());\n  sma = new Sma(period);\n  ema = new Ema(period);\n  hma = new Hma(i32(p_hull_period()));\n  wma = new Wma(period);\n  alma = new Alma(period);\n  swma = new Swma();\n  vwma = new Vwma(period);\n  rma = new Rma(period);\n  linreg = new Linreg(period, 0.0);\n  bb = new Bb(period, p_mult());\n  kc = new Keltner(period, p_kc_mult(), i32(p_atr_period()));\n  dc = new Donchian(period);\n}\n\nexport function state(): i32 {\n  const close = in_close();\n  const high = in_high();\n  const low = in_low();\n  smaValue = sma.update(close);\n  emaValue = ema.update(close);\n  hmaValue = hma.update(close);\n  wmaValue = wma.update(close);\n  almaValue = alma.update(close);\n  swmaValue = swma.update(close);\n  vwmaValue = vwma.update(close, in_volume());\n  rmaValue = rma.update(close);\n  linregValue = linreg.update(close);\n  bb.update(close);\n  kc.update(close, high, low, close);\n  dc.update(high, low);\n  // Donchian is finite from the first bar, so the row is ready as soon as it has computed;\n  // the slower lines simply write NaN until their own windows fill.\n  return 1;\n}\n\nexport function finalize(): void {\n  out_sma(smaValue);\n  out_ema(emaValue);\n  out_hma(hmaValue);\n  out_wma(wmaValue);\n  out_alma(almaValue);\n  out_swma(swmaValue);\n  out_vwma(vwmaValue);\n  out_rma(rmaValue);\n  out_linreg(linregValue);\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n  out_kc_upper(kc.upper);\n  out_kc_basis(kc.basis);\n  out_kc_lower(kc.lower);\n  out_dc_upper(dc.upper);\n  out_dc_basis(dc.basis);\n  out_dc_lower(dc.lower);\n  emitRow();\n}\n\nexport function reset(): void {\n  sma.reset();\n  ema.reset();\n  hma.reset();\n  wma.reset();\n  alma.reset();\n  swma.reset();\n  vwma.reset();\n  rma.reset();\n  linreg.reset();\n  bb.reset();\n  kc.reset();\n  dc.reset();\n  smaValue = NaN;\n  emaValue = NaN;\n  hmaValue = NaN;\n  wmaValue = NaN;\n  almaValue = NaN;\n  swmaValue = NaN;\n  vwmaValue = NaN;\n  rmaValue = NaN;\n  linregValue = NaN;\n}\n```\n\nThe whole module is one chart overlay with eighteen legend entries; on\nyour machine every one of them is a metric id (`wrun/@you/\u003Cname>/hma`,\n`.../bb_upper`, and so on) that an alert or a screen can read.\n\n## Warm-up and named streams\n\nTwo ideas worth seeing on their own: an average is blank until its window\nfills, and a band's three levels are three independent outputs you can\ndraw or hide one at a time. The Bollinger edges below are drawn while the\nbasis stays data-only (`none`): it still computes, still exists as a\nmetric, and the chart shows only the two bands. All three begin together\nonce the 20-bar window completes, because one `Bb` feeds them.\n\n```typescript\nimport { input, line, none, ohlcv, output, overlay, param } from \"./sdk/declare\";\nimport { in_close } from \"./gen/inputs\";\nimport { emitRow, out_bb_basis, out_bb_lower, out_bb_upper, out_sma20 } from \"./gen/outputs\";\nimport { p_period } from \"./gen/params\";\nimport { Bb, Sma } from \"./sdk/ta\";\n\nparam(\"period\", 20, { min: 2, max: 400 });\ninput(\"close\", ohlcv.close);\noutput(\"sma20\", line, overlay, { color: \"#2563eb\", width: 2, description: \"NaN until the window is complete\" });\noutput(\"bb_upper\", line, overlay, { color: \"#16a34a\", width: 2, description: \"Bollinger upper band\" });\noutput(\"bb_basis\", none, overlay, { description: \"Computed, never drawn: a metric without a line\" });\noutput(\"bb_lower\", line, overlay, { color: \"#dc2626\", width: 2, description: \"Bollinger lower band\" });\n\nlet sma = new Sma(20);\nlet bb = new Bb(20, 2.0);\nlet value: f64 = NaN;\n\nexport function init(): void {\n  sma = new Sma(i32(p_period()));\n  bb = new Bb(i32(p_period()), 2.0);\n}\n\nexport function state(): i32 {\n  const close = in_close();\n  value = sma.update(close);\n  bb.update(close);\n  // Abstain the whole row while the window is filling: no legend value, no metric row, nothing drawn.\n  return isNaN(value) ? 0 : 1;\n}\n\nexport function finalize(): void {\n  out_sma20(value);\n  out_bb_upper(bb.upper);\n  out_bb_basis(bb.basis);\n  out_bb_lower(bb.lower);\n  emitRow();\n}\n\nexport function reset(): void {\n  sma.reset();\n  bb.reset();\n  value = NaN;\n}\n```\n\n## Alma and Swma boundaries\n\n`Alma`'s omitted `offset` and `sigma` default to `0.85` and `6`, so a\ndefault construction and an explicit one agree to the last bit; `Swma`\nuses the fixed four-tap weighting, so it agrees with the arithmetic\nspelled out by hand over the last four closes. The module below computes\nboth forms and writes each line only where the class agrees with the\nmanual form, which is every bar once the windows are warm: a `NaN`\nwritten on a disagreeing bar would leave a visible hole.\n\n```typescript\nimport { input, line, lower, ohlcv, output, param } from \"./sdk/declare\";\nimport { in_close } from \"./gen/inputs\";\nimport { emitRow, out_alma_check, out_swma_check } from \"./gen/outputs\";\nimport { p_length } from \"./gen/params\";\nimport { Alma, Swma } from \"./sdk/ta\";\n\nparam(\"length\", 10, { min: 2, max: 200 });\ninput(\"close\", ohlcv.close);\noutput(\"alma_check\", line, lower, { color: \"#2563eb\", width: 2, description: \"ALMA with the default offset 0.85 and sigma 6\" });\noutput(\"swma_check\", line, lower, { color: \"#16a34a\", width: 2, description: \"SWMA against the four-tap arithmetic\" });\n\nlet almaDefault = new Alma(10);\nlet almaExplicit = new Alma(10, 0.85, 6.0);\nlet swma = new Swma();\n// The manual SWMA keeps the last four closes by hand: x0 is the newest.\nlet x0: f64 = NaN;\nlet x1: f64 = NaN;\nlet x2: f64 = NaN;\nlet x3: f64 = NaN;\nlet almaCheck: f64 = NaN;\nlet swmaCheck: f64 = NaN;\n\nexport function init(): void {\n  almaDefault = new Alma(i32(p_length()));\n  almaExplicit = new Alma(i32(p_length()), 0.85, 6.0);\n  swma = new Swma();\n}\n\nexport function state(): i32 {\n  const close = in_close();\n  const a = almaDefault.update(close);\n  const b = almaExplicit.update(close);\n  const s = swma.update(close);\n  x3 = x2;\n  x2 = x1;\n  x1 = x0;\n  x0 = close;\n  const manual = (x3 + 2.0 * x2 + 2.0 * x1 + x0) / 6.0;\n  almaCheck = Math.abs(a - b) \u003C 0.000001 ? b : NaN;\n  swmaCheck = Math.abs(s - manual) \u003C 0.000001 ? s : NaN;\n  return isNaN(almaCheck) && isNaN(swmaCheck) ? 0 : 1;\n}\n\nexport function finalize(): void {\n  out_alma_check(almaCheck);\n  out_swma_check(swmaCheck);\n  emitRow();\n}\n\nexport function reset(): void {\n  almaDefault.reset();\n  almaExplicit.reset();\n  swma.reset();\n  x0 = NaN;\n  x1 = NaN;\n  x2 = NaN;\n  x3 = NaN;\n  almaCheck = NaN;\n  swmaCheck = NaN;\n}\n```\n\n## What changed from kScript\n\n- A builtin call (`sma(source=close, period=20)`) became an object you\n  own: construct it in `init()`, keep it in a module-level `let`, feed it\n  in `state()`. There is no series to pass in; the class sees one value per\n  bar, which is the whole [execution model](../core-concepts/execution-model.md).\n- A band's `.upper` / `.basis` / `.lower` streams became three fields read\n  after `update()` and three outputs. Nothing indexes into a tuple.\n- `vwma(source=trade)` reading volume off an OHLC series became an explicit\n  `input(\"volume\", ohlcv.volume)` and a two-argument `update(price,\n  volume)`: an Indicator names every field it reads.\n- Warm-up stays `NaN`, and `NaN` propagates through arithmetic exactly as\n  `na` did. `isNaN(x)` is the test; there is no `nz` builtin, but a\n  two-line helper is on the [Series functions](series-functions.md) page.\n- The numbers are the engine's numbers: every class here matches the\n  kScript engine bar for bar, so a port is a rename, not a re-tune. 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